Question

Given that f(-0.5)=2 and f'(-0.5)=4, use a tangent line approximation to estimate f(0).
The lesson is not very clear on what a tangent line approximaton is.

Answer 1

The tangent line approximation is:
f(x) = f(a) + (x-a)*f'(a)
It is the formula for a straight line that goes through x = a with the slope of f(x) at x=a.

Let a = -0.5 and x = 0
f(0) = 2 + (0.5)*4 = 4